On Klass' series criterion for the minimal growth rate of partial maxima (Q1821424)
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scientific article; zbMATH DE number 3998884
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Klass' series criterion for the minimal growth rate of partial maxima |
scientific article; zbMATH DE number 3998884 |
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On Klass' series criterion for the minimal growth rate of partial maxima (English)
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1987
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Consider a sequence \(\{X_ i\}\) of i.i.d. random variables and let \(M_ n=\max (X_ 1,...,X_ n)\) be the maximum of the first n of the \(X_ i\). The author gives a martingale based proof of the theorem due to \textit{M. J. Klass} [Ann. Probab. 13, 1369-1370 (1985; Zbl 0576.60023)] that P \(\{M_ n\leq b_ n\) \(i.o.\}=1\) iff \(\sum^{\infty}_{1}P(X_ 1>b_ n)\exp (-n P(X_ 1>b_ n))=+\infty\).
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partial maxima
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Borel-Cantelli lemma
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